# A Guide to Game Theory

As we all know, game theory is a branch of mathematics that deals with the mathematical analysis of strategic interactions between agents, typically in games. The theory has been used in various applications, from economics to computer science.

One of the most famous applications of game theory is the prisoner’s dilemma, which von Neumann and Morgenstern first described in 1944. The prisoner’s dilemma is a two-person game in which players choose between betraying their partner or staying loyal. If both players betray their partner, both players get a Prisoner’s Dilemma payoff of zero; if only one player betrays, the betrayer gets a payoff of two while the loyal player gets a payoff of one. If both players stay loyal, both players get a payoff of one. But if only the betrayer defects, the betrayer gets a payoff of three, while the loyal player gets a zero payoff. Thus, the rational choice for the betrayer is to defect almost always.

The theory of game theory has been used to study a wide range of situations, from strategic problems in business to the interactions between predators and prey in nature. One of the most important applications of game theory is the study of bargaining, in which agents try to reach an agreement. Game theory has also been used to study political decisions like voting and coalition formation.

Overall, game theory is an extremely important tool for understanding human behavior. It has been used to study a wide range of situations, from the interactions between agents in the business to the political decisions we make every day.